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Lewis's (1973a) semantics for counterfactuals conditionals has been highly popular, at least among those philosophers who believe that counterfactuals have truth-conditions. According to his semantics, a counterfactual is nonvacuously true in the actual world if and only if there is a possible world where both its antecedent and its consequent are true that is closer to the actual world than any worlds where its antecedent is true while its consequent is false. In addition to this semantics, Lewis gives an account of the closeness relation that is at work there. This closeness relation is to be understood as a relation of comparative overall similarity: a possible world w is closer to the actual world than a possible world v if and only if w is more similar overall to the actual world than v is. The overall similarity between worlds, Lewis holds, is a function of different aspects of similarity between worlds, just as, say, the overall similarity between people is a function of different aspects of similarity between people (1973c: 420-21). So far we do not disagree with Lewis. We shall argue, however, that the relation of comparative overall similarity cannot be a function of mere relations of comparative aspectual similarity for very general reasons. If aspects of similarity are to determine overall similarity, we have to make additional assumptions about how these aspects are measured on pain of falling prey to an application of Arrow's impossibility theorem.